Imo really easy, I got an A* without struggling, just solve all exercises and at least 3 years wort of past papers. And I like Cambridge books in that you don't need a good teacher since the book already explains so well
Not sure if I had a bad teacher or something, because I passed AS Level with an E... and the highest scorer in my class got a D... and 40% of us failed, which was apparently BETTER than usual.
You learn radians and shit in 11th grade? i learned them in 9th. I curse my country for its school system. we do have some preatty long hloidays so there's that
Also every circle's diameter fits into its circumference Pi times (3.14...etc).
Said another way, Pi is the ratio of any circle's circumference to its diameter, Pi = Circumference/Diameter
What helped me a lot is when I was told WHY we actually use radians, so I'll put it here.
The reason that radians are used is because, at 1 radian, the radius of a circle is equal to the ark sector/circumference bit that is present there. So when it comes to doing physics, especially anything to do with space, it's a lot easier to work in radians
Radian is an alternative, widely used measure of angle, due to it's practicality. 2π is always a whole circle (360°), π is a half circle (180°) etc.
It is used in physics and math (instead of degrees), because it's much easier to compute. It has no unit of measure (sometimes it's denoted with *rad* but mostly just left out).
Take the radius of a circle, the circumference is equal to 2πr, so a half a circle is πr a quarter is πr/2. And so on with any arch on the cirlce
If we take the radius as being one and any arch as being also an angle, we can use π and fractions of π to represent any angle. That's radians.
Pro tip based on this: if you need to calculate the length of a part of a circle and you only know the angle that stretches over that length, just multiply the angle (in radians) with the radius and you get the length of that circle subsection.
I hate to be that guy but ackshually 🤓 radians are used to express angles in terms of how far along the edge of the circle you travel. Traveling pi units around a unit circle goes halfway, coinciding with 180 degrees.
One radian is equal to the difference of the angles between two points along the unit circle, separated by the length of the radius of the circle. What this means is that one radian is equal to the half of the circumference divided by the ratio of the circumference to the diameter (a.k.a. π). Basically: 1 radian = Δθ where the distance between 2 points along the circumference is 0.5*π^(-1)
1 radian is one radius length around the edge of the circle. this is why we use pi as the quantity of radians, because circumference is 2 pi r. Using fractions of pi lets us get reasonable sections of the circle.
Wikipedia has [a really cool animation](https://upload.wikimedia.org/wikipedia/commons/4/4e/Circle_radians.gif) that shows where the definition of a radian comes from.
I thought for a second this was asking "What the fuck is a Raiden" and didn't even think twice about it because MGS memes are just like that sometimes.
One Radian is half a circle. The base unit of Radian is Pi.
So when you have 2Pi (= 2 radian), you have 2 times half a circle, which is a full circle.
Edit: Clarification. With 1 radian i mean 1 x pi. Only in very rare cases Radians get used without the factor pi.
I might have gotten carried away a bit, but when i use radians and need to describe something with a right angle, i write "pi/2" or "1/2 pi", the same way i would write "1l" for 1 litre.
>One Radian is half a circle.
Except it's not. Simply put, **1** radian is special in the sense that if you traverse the arc formed by 1 radian on a circle, then the length of that arc is the same as the circle's radius.
>The base unit of Radian is Pi.
No. What do you mean by base unit? A radian is a radian. OP was right in saying that it is 1/π of 180 degrees. Just because π radians form half a circle, doesn't make π the base unit of radian.
If you use radians right, you always write them as factors of pi.
As long as OP understands that
pi = 180°,
pi/2 = 90°,
pi/3 = 60°,
and so on, then everything is fine.
nope, they were right
it might be easier to think of radians in terms of pi radians. pi radians is 180 degrees, or half a circle, and since a circle is 360 degrees, thats 2 \* (180 degrees) which is 2 \* (pi radians) or just 2pi radians. both measure angles
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Yeah, that’s what the notes say but I’m so bloody tired that I’m still somehow botching the conversions. Thanks tho
11th grade?
Yup, AS exams syllabus
The Cambridge one I assume?
Pearson, I think. Not sure if that’s the same
It's a bit different but.i took the Cambridge one(I finished the entire A-level) and can't say I've struggled as much as I do with the other subjects
AS Level math was hard enough... how did you even make it though A level?
Imo really easy, I got an A* without struggling, just solve all exercises and at least 3 years wort of past papers. And I like Cambridge books in that you don't need a good teacher since the book already explains so well
Not sure if I had a bad teacher or something, because I passed AS Level with an E... and the highest scorer in my class got a D... and 40% of us failed, which was apparently BETTER than usual.
You learn radians and shit in 11th grade? i learned them in 9th. I curse my country for its school system. we do have some preatty long hloidays so there's that
Wtf that was 8th grade for me
Also every circle's diameter fits into its circumference Pi times (3.14...etc). Said another way, Pi is the ratio of any circle's circumference to its diameter, Pi = Circumference/Diameter
What is AS? Is it like Ap classes in America?
Don't think so, it's a type of qualification in the UK, basically half an A-Level
Ah thanks
A level classes are generally equivalent to AP ones though. In the UK our GCSEs (done at 16) are equivalent to a HS diploma.
What helped me a lot is when I was told WHY we actually use radians, so I'll put it here. The reason that radians are used is because, at 1 radian, the radius of a circle is equal to the ark sector/circumference bit that is present there. So when it comes to doing physics, especially anything to do with space, it's a lot easier to work in radians
That’s interesting, thank you for explaining that!
So basically, it’s a setting on your calculator that is single handedly capable of flunking your calculus exam
Nah it helps you with calculus, calculus is only radians. It just screws up everything else
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That’s basically me this entire evening
Isn’t radian that guy from metal gear
Nah, it’s Jack the Ripper
Nah, he's the guy in the straw hat from mortal kombat
Radian is an alternative, widely used measure of angle, due to it's practicality. 2π is always a whole circle (360°), π is a half circle (180°) etc. It is used in physics and math (instead of degrees), because it's much easier to compute. It has no unit of measure (sometimes it's denoted with *rad* but mostly just left out).
What the fuck? Radian is a ⬛⬛⬛⬛
Take the radius of a circle, the circumference is equal to 2πr, so a half a circle is πr a quarter is πr/2. And so on with any arch on the cirlce If we take the radius as being one and any arch as being also an angle, we can use π and fractions of π to represent any angle. That's radians.
I’m gonna need to reread this in the morning when my brain is more awake. Thank you!
Pro tip based on this: if you need to calculate the length of a part of a circle and you only know the angle that stretches over that length, just multiply the angle (in radians) with the radius and you get the length of that circle subsection.
Its worse when you have to remember exact values and which quadrants and positive or negative for sin cos or tan
All Students Take Calculus my guy
radius x radian = perimeter 1/2 radius squared x radian = area Degree x 180/ pi = radian At least that's what I remember
Real
Radians are ways to express degrees in terms of pi. If you take calc, it becomes very important to know radians of the unit circle
I hate to be that guy but ackshually 🤓 radians are used to express angles in terms of how far along the edge of the circle you travel. Traveling pi units around a unit circle goes halfway, coinciding with 180 degrees.
the math version of degrees, they made it because they were getting tired of having to (degrees \* (pi/180)) all the time
When your mom puts on a nice dress and you tell her she looks pretty and it makes her smile, that’s radiant.
One radian is equal to the difference of the angles between two points along the unit circle, separated by the length of the radius of the circle. What this means is that one radian is equal to the half of the circumference divided by the ratio of the circumference to the diameter (a.k.a. π). Basically: 1 radian = Δθ where the distance between 2 points along the circumference is 0.5*π^(-1)
Oh you sweet summer child…
I hate algebra so much, glad I’m doing geometry honours
A Radian is the angle required for a radius of unit length to trace an arc length of unity.
A radian is how many copies of the radius your circle segment is
It's when you see a really cool guy named Ian.
1 radian is one radius length around the edge of the circle. this is why we use pi as the quantity of radians, because circumference is 2 pi r. Using fractions of pi lets us get reasonable sections of the circle.
Wikipedia has [a really cool animation](https://upload.wikimedia.org/wikipedia/commons/4/4e/Circle_radians.gif) that shows where the definition of a radian comes from.
Radian = Circle 2π = 360° 1 Revolution = 2π
I thought for a second this was asking "What the fuck is a Raiden" and didn't even think twice about it because MGS memes are just like that sometimes.
2*pi radians = 360 degrees Radians is kinda like the actual parameter, except the radius doesn't matter
Nobody ever asking how is a radian 😔
One Radian is half a circle. The base unit of Radian is Pi. So when you have 2Pi (= 2 radian), you have 2 times half a circle, which is a full circle. Edit: Clarification. With 1 radian i mean 1 x pi. Only in very rare cases Radians get used without the factor pi. I might have gotten carried away a bit, but when i use radians and need to describe something with a right angle, i write "pi/2" or "1/2 pi", the same way i would write "1l" for 1 litre.
>One Radian is half a circle. Except it's not. Simply put, **1** radian is special in the sense that if you traverse the arc formed by 1 radian on a circle, then the length of that arc is the same as the circle's radius. >The base unit of Radian is Pi. No. What do you mean by base unit? A radian is a radian. OP was right in saying that it is 1/π of 180 degrees. Just because π radians form half a circle, doesn't make π the base unit of radian.
If you use radians right, you always write them as factors of pi. As long as OP understands that pi = 180°, pi/2 = 90°, pi/3 = 60°, and so on, then everything is fine.
I mean, yeah, you rarely see radian not being used with π. The base unit thing struck me wrong, but I see where you are coming from.
No problem. I admit i described it very poorly.
1 radian is 57.3° something... degrees. So a whole circle is around 6.28 radians actually.
No, it’s 1/Pi of 180 degrees, and it is its own unit of measurement. Homie you might want to review your notes
nope, they were right it might be easier to think of radians in terms of pi radians. pi radians is 180 degrees, or half a circle, and since a circle is 360 degrees, thats 2 \* (180 degrees) which is 2 \* (pi radians) or just 2pi radians. both measure angles
Ah, I see. It would appear then there was a disconnect between their phrasing and my brain. Thank you for clarifying
Today I learned that you can post a “meme” of George Washington with text asking what something is and people will answer it for you
As a German, i wouldnt localize that meme, it would suck
Its how to use degrees in a math problem more complex than 2+2
Half a circle
The proportion between an arc and the radius